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Hamming, Richard W.
Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.
In N. Rose Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Hamilton, Sir William Rowan (1805-1865)
On earth there is nothing great but man; in man there is nothing great but mind.
Lectures on Metaphysics.
Hamilton, Sir William Rowan (1805-1865)
I regard it as an inelegance, or imperfection, in quaternions, or rather in the state to which it has been hitherto unfolded, whenever it becomes or seems to become necessary to have recourse to x, y, z, etc.
In a letter from Tait to Cayley.
Hamilton, [Sir] William Rowan (1805-1865)
Who would not rather have the fame of Archimedes than that of his conqueror Marcellus?
In H. Eves Mathematical Circles Revisited, Boston: Prindle, Weber and Schmidt, 1971.
Halmos, Paul R.
To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.
I Want to Be a Mathematician, Washington: MAA Spectrum, 1985.
Halmos, Paul R.
Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
I Want to Be a Mathematician, Washington: MAA Spectrum, 1985.
Halmos, Paul R.
The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me -- both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.
I Want to Be a Mathematician, Washington: MAA Spectrum, 1985.
Halmos, Paul R.
[T]he source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case.
I Want to Be a Mathematician, Washington: MAA Spectrum, 1985.
Halmos, Paul R.
I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."
I Want to Be a Mathematician, Washington: MAA Spectrum, 1985, p. 120.
Halmos, Paul R.
[T]he student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."
I Want to Be a Mathematician, Washington: MAA Spectrum, 1985.

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